Avoiding the question I asked?PeteOlcott wrote: ↑Fri May 10, 2019 2:11 amIt sure as Hell makes much more sense than saying that every truth is logically

entailed by either falsehood or contradiction.

## Search found 781 matches

- Fri May 10, 2019 3:33 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2530**

### Re: Possible consequences of falsifying the principle of explosion?

- Fri May 10, 2019 12:13 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2530**

### Re: Possible consequences of falsifying the principle of explosion?

I would correct it to conform to the English meaning this way: Logical implication p q p ⇒ q T T T T F F F T F F F F Isn't that what everyone else calls logical AND? Would you say that * 2 + 2 = 4 and George Washington is regarded as the father of his country. and * 2 + 2 = 4 THEREFORE George Washi...

- Wed May 08, 2019 12:47 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Possible consequences of falsifying the principle of explosion?
- Replies:
**86** - Views:
**2530**

### Re: Possible consequences of falsifying the principle of explosion?

Instead of undecidable logic sentences "proving" incompleteness of formal systems they are merely rejected as derived from unsound deduction. That doesn't make any sense. If a sufficiently interesting system is consistent, it must necessarily contain closed wffs that can neither be proven nor dispr...

- Sat May 04, 2019 7:38 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Converting formal proofs to conform to sound deduction
- Replies:
**30** - Views:
**1730**

### Re: Converting formal proofs to conform to sound deduction

Copyright ???? Pete Olcott It's not a legal copyright without a year. When I was a tech writer (a very long time ago) I learned to write "Copyright (C) 1920 Thomas Edison Company" in exactly that format. Just some free legal advice. And of course I'm not a lawyer and the law might have changed sinc...

- Fri May 03, 2019 4:23 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Converting formal proofs to conform to sound deduction
- Replies:
**30** - Views:
**1730**

### Re: Converting formal proofs to conform to sound deduction

mortal adjective of a living human being often in contrast to a divine being subject to death. Thanks for clarifying your thinking. You are making the point that under your understanding of logic, we should analyze the word "mortal" and so forth. I'd submit that if you show the phrase "All men are ...

- Thu May 02, 2019 7:14 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Tarski Undefinability Theorem Succinctly Refuted
- Replies:
**106** - Views:
**2376**

### Re: Tarski Undefinability Theorem Reexamined

... it says what it says - it does what it does. I think I'm going to go with ... not convinced that you have any idea what category theory is. It's no great shame. You could say something like, "Cool, I've heard about category theory but don't know much about it. Tell me more." Or even, "F*** you,...

- Wed May 01, 2019 12:54 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Converting formal proofs to conform to sound deduction
- Replies:
**30** - Views:
**1730**

### Re: Converting formal proofs to conform to sound deduction

I mean it in the sense where "are" means ⇔ Oh well that explains your "all X are Y" remark. Classically "All men are mortal" means ==> and not <==>, we agree on that I hope. So if you said, "All X are Y and all Y are X" you'd at least have identity between sets. That would have been more clear to a...

- Wed May 01, 2019 12:46 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Tarski Undefinability Theorem Succinctly Refuted
- Replies:
**106** - Views:
**2376**

### Re: Tarski Undefinability Theorem Reexamined

You have not convinced me that when we talk about category theory we are talking about the same thing.Logik wrote: ↑Wed May 01, 2019 12:02 amIt's a formalization of Equifinality.

https://en.wikipedia.org/wiki/Equifinality

- Tue Apr 30, 2019 11:40 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Tarski Undefinability Theorem Succinctly Refuted
- Replies:
**106** - Views:
**2376**

- Tue Apr 30, 2019 11:27 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Converting formal proofs to conform to sound deduction
- Replies:
**30** - Views:
**1730**

### Re: Converting formal proofs to conform to sound deduction

Really? So when I say "All cats are mammals" that's the same as saying cats are isomorphic to mammals? OK. so you are using "are" to mean "subset of". Cool. We can play that game right until we get to the set of all sets. And then I am going to ask you.... This isn't just wrong on the facts, it's m...

- Tue Apr 30, 2019 11:03 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Converting formal proofs to conform to sound deduction
- Replies:
**30** - Views:
**1730**

### Re: Converting formal proofs to conform to sound deduction

To say ALL X are Y is to say "there is an isomorphism between X and Y". And that only works in formal systems. Really? So when I say "All cats are mammals" that's the same as saying cats are isomorphic to mammals? This isn't just wrong on the facts, it's meta-wrong. It's a category error. It's not ...

- Sat Apr 27, 2019 1:05 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)
- Replies:
**33** - Views:
**698**

### Re: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)

I am gratified to have made my point.PeteOlcott wrote: ↑Sat Apr 27, 2019 1:02 amI think these things through more deeply as I get more feedback.

- Sat Apr 27, 2019 12:33 am
- Forum: Logic and Philosophy of Mathematics
- Topic: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)
- Replies:
**33** - Views:
**698**

### Re: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)

If person Y could come up with some set of axioms such as PA that make their stipulation coherent (such as the distinction between Euclidean and non-Euclidean geometry) then it would be acceptable. I said nothing about PA. In fact these are one-sentence axiom systems . The entirety of the axiom sys...

- Fri Apr 26, 2019 11:52 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)
- Replies:
**33** - Views:
**698**

### Re: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)

Person X stipulates the axiom 2 + 2 = 4. Person Y stipulates the axiom 2 + 2 = 5. Are both axioms true by virtue of being axioms? I think that most people would agree that person Y would be a liar for directly contradicting mutually agreed upon conventions. Then you agree that the truth value of a ...

- Fri Apr 26, 2019 7:10 pm
- Forum: Logic and Philosophy of Mathematics
- Topic: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)
- Replies:
**33** - Views:
**698**

### Re: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)

You ignored my question.PeteOlcott wrote: ↑Fri Apr 26, 2019 5:55 pmI know that my premises are true because they are semantic tautologies:

Person X stipulates the axiom 2 + 2 = 4.

Person Y stipulates the axiom 2 + 2 = 5.

Are both axioms true by virtue of being axioms?